Resulting M_BH–M_star scaling relation from the continuity equation. Left: z evolution of the scaling relations from z = 0 (darker) to z = 5 (lighter). At each redshift, the dashed line style indicates the regime above the 99% stellar mass limits (assuming Weaver et al. 2023 COSMOS2020 stellar mass function and an area of 24 deg²), above which the M_BH − M_star relation is to be considered an extrapolation. The dotted line shows the assumed initial conditions at z = 5.5 (Reines & Volonteri 2015). Right: Local relation implied by the continuity equation (black line). The shaded region corresponds to an assumed scatter of Δlog₁₀(M_BH/M_⊙) = 0.50 dex. The other non-solid lines correspond to local and inactive early-type galaxies (Häring & Rix 2004; Kormendy & Ho 2013), local AGNs (Reines & Volonteri 2015), the de-biased relation from SDSS galaxies (Shankar et al. 2016), and major-merger built S0 and E galaxies (Graham 2023).